That's very negative thinking, Jim, though I see what you mean.
I don't have a problem with a senator running for (vice-)president. However, a governor is part of the 'executive' branch (even though elected). Things to consider: Who runs the state at the moment? If the state runs itself, abolish governors. Besides, you dupe the electorate by running for another office in mid-term. There are other, policy-related, issues as well.